A058541 Trajectory of 1 under map that sends x to 3x - sigma(x).
1, 2, 3, 5, 9, 14, 18, 15, 21, 31, 61, 121, 230, 258, 246, 234, 156, 76, 88, 84, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28
Offset: 0
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Mathematica
NestList[3#-DivisorSigma[1,#]&,1,70] (* Harvey P. Dale, Jul 23 2012 *)